I’ve noticed that lately guys like Roy Spencer have been spending a lot of time trying to establish some kind of minimum level for what is unquestionably true about AGW. It seems as if some of the more serious skeptics are beginning to worry that their whole cause will degenerate into another anti-science conspiracy theory that isn’t taken serious outside a small circle of believers.

I assume comment 10 is a joke. And so is comment 9, I’m guessing as well. Either point of view is basically stupid enough to not make it worth the time to make the point. The temperature of water is directly related to the energy in the water. If you add a joule of energy, you don’t have to wait a while for the temperature to rise a corresponding amount. The reason it takes a pot of water a while to reach its new temperature is because the stove top is a particularly inefficient way to add heat to water. Is there really someone who thinks that if you stop adding heat energy to water, the temperature will continue to rise?

Yes, but Willis Eschenback doesn’t think phytoplankton are declining because he personally hasn’t seen any evidence that the higher level biomass in the oceans is declining. I guess the word “overfishing” and phrase “overexploited fisheries” aren’t in his lexicon.

um..George..shake thy head and see if anything falls out your ears.
Of course stove top heating “is a particularly inefficient way to add heat to water.”
So is the Sun, you know our star, rather inefficient at adding heat to water.
That’s the whole bloody point.
What do you use to heat your kettle?
Thermo nuclear weapons?

I got my high school education in science by going to high school. Not by starting a McCarthyite campaign against weather stations. If Watts is learning basic science, that’s all to the good, I suppose.

His reply falls into the “correct but useless” pedantic category. Yes, the energy you supply will heat the water pretty much immediately, but you CAN’T supply all the energy in one go and that was (almost certainly) the point of the original poster.

Simplified example: My electric kettle consumes 2kW of electrical power when on. If I want to boil 1l of water it takes about 4190J to heat it one degree celsius. So in one second it heats the water 0.48 degree (assuming the water is well-stirred, no heat losses, yada,yada). Heating from 10 degrees (cold tap) to boiling will take a little over 3 minutes. Now, I could heat the water to boiling in a millisecond if only I could draw 377MW from the grid. Don’t try that at home.

Well written but based on which Earth system model? Richard Courtney is right but seems ignorant of the input the deep hot biosphere is putting into the Engelebeen carbon cycle. That alone sinks the AGW idea.

“Of course water instantly gains absolute temperature and has no heat capacity.”

Oh bugger.

Here, let’s go through both sides and show what’s going on and then why this is so very silly.

1) Yes, temperature will rise instantly if you add energy to something.
2) To reach a new equilibrium temperature when increasing power supplied to heating takes time because of the need to transport the heat evenly to create an energy balance.

OK?

Now in case #1, the temperature is badly defined. In the example of a stove, there’s water that is bubbling (100C) and water that isn’t (less than 100C). Therefore there’s bits of water at different temperatures and there is no “temperature” of the entire thing.

In that case, you could instead work with average temperature or, more scientifically useful, the temperature at which the energy content is equal.

Why is this thread become so silly?

Because depending on what you mean by temperature, either is true. But then you have to explain which temperature you mean. The first quote was obviously about a new temperature equilibrium, not new temperature increases.

What’s made it even sillier is the above quote.

You don’t have zero heat capacity to make instantaneous temperature changes. Heat capacity is how much temperature rises with energy. Zero heat capacity would mean infinite temperatures instantaneously. No instantaneous finite heating.

Tom, I take it back. However, maybe it would help if you just told us what the hell you were talking about before anyone made the silly leap to try to address one of your comments about tea or nuclear weapons.

Wow: I think he believes bacteria deep, deep into the earth’s crust really are responsible for everything that appears to indicate CO2 is a problem/humans are responsible/the earth will warm/it will matter.

Eli Rabett also had a post up recently, with some amusing quotes from prominent denialists having to disappoint their fellow travelers on some of the more wacky extravagant theories. Even Monckton gets blasted from the right occasionally, which isn’t a surprise, but that he takes the time to reply is.

I wonder why it’s happening now, of all times? Maybe Exxon is threatening to cut funding

Amanda, you are close, but not quite there. I think you need to look up what ‘heat capacity’ really means. It doesn’t mean that you can add heat energy without the temperature changing. It is meant to be a measure of how much the temperature changes when heat energy is added (just for clarity, this is as opposed to other types of energy, like potential, kinetic, chemical, etc.). When heat energy is added to water, its temperature changes immediately. Yes, that’s right, immediately. One of the reasons why water is chosen as a coolant or insulator (and there are many that have nothing to do with its heat capacity) is that with a high heat capacity, you can add a lot of heat with the temperature only changing a little. But don’t forget, when you add that heat energy, the temperature changes right away. By the definition of the word ‘temperature’ it changes instantaneously. Remember, temperature is a measure of heat energy. Temperature and heat energy are the same thing.

Wow made a good point. This discussion of temperature and heat capacity is rather silly. People should really be talking about how well mixed the climate is, and what the term ‘in the pipeline’ means and how well, if at all, temperature rise that is ‘in the pipeline’ can be predicted.

It’s quite a spectacle seeing the Wattards arguing over what should be such an easily accepted fact. Next they’ll be arguing that burning fossil fuel does not produce CO2 at all.

But I have to say that, strictly speaking, it is logically possible for Courtney and Birch to be correct, i.e., the atmospheric increase could be happening independently of fossil fuel combustion. The problem, of course, is that they then have to describe the path that fossil fuel CO2 takes, explain all the evidence showing that the oceans are a net sink, and explain why the parallel increases in atmospheric CO2 and fossil fuel combustion are somehow nothing more than an amazing coincidence.

George requested what in the pipeline means, and how it relates to the heat capacity.

In short, there is currently a global radiative imbalance (more energy absorbed than emitted), which raises ocean water temperature slowly (but pretty steadily globally at the surface). Balance will be achieved when the outgoing radiation increases due to reaching a final higher temperature. This final temperature compared to current is the warming in the pipeline, caused by the current CO2 composition.

He’s also the same Richard S Courtney who went in to bat for Louis Hissink when Hissink claimed, on that same thread, that “no gas can store energy”. His excursion into that dead-end was much shorter than cohenite’s painful limping along that path though, probably because Courtney could see that cohenite and Hissink were staggering on their knees.

Thank you Wow @ 19.
Your explaination is how I understand this item, but all too often, what I understand is incapable of getting through to my finger tips.
I think I should stay away from the keyboard for a bit and go back on listening/learning mode.
I have a bit of a sore back right now and I’m on the irritable side at the moment so apologies for any snark.

As to the thermo discussion… Heat capacity is a red herring. The key is that while temperature is a function of energy, the relevant quantity in equilibruim is power, i.e. it’s radiative power that’s a function of temperature.

An increment of greenhouse gas results in an instantaneous change not in energy but in the time derivative of energy.

In terms of the wacky astrologer an interesting thing happened on the Guardian today. Turns out one of the more biosterous posters about his new weather application for apple is probibly the person who developed it. One or two the usual peeps over there did a bit of websearching and the company that did the development is 4 months old and only seems to have one product out. The Watts one.

What you have to understand is that Climategate changed the rules. The Lindzens, Pielkes and Spencers are no longer free to lead a double life, casting crap on their scientific colleagues in the Wall Street Journal, WUWT, and so on without losing all respect in the scientific community.

> An increment of greenhouse gas results in an instantaneous change not in energy but in the time derivative of energy.

I have a graduate degree in engineering and a not insignificant experience with calculus, but I have no idea what this means. Are you saying that we can change the ‘amount of energy something has over a period of time’ (“the time derivative of energy”) without changing the amount of energy something has? Unless you changed to the time derivative of energy to zero, how is this possible?

What this sounds like is hand waving to try to explain ‘temperature change in the pipeline’. If I’m wrong, I’m sorry and willing to admit it if you could clarify for me.

There is no such as temperature change ‘in the pipeline’. If the earth is absorbing more solar energy than it is radiating away, that energy is getting stored somewhere.

delta Q = Qin – Qout

At equilibrium, Qin and Qout are equal. If our planet is not at equilibrium, then delta Q is positive. My understanding of the currently accepted theory is that the temperature of the planet will increase until a new equilibrium Qout is reached. If we assume that Qin has not changed, then what has been happening all along is that Qout has been lowered by the effects of CO2 in the atmosphere. As the temp of the planet increases, Qout will have a corresponding increase, as the effects of CO2 are overcome by the increased temperature of the planet.

So, one of the current issues is to figure out how this deltaQ is being stored. If the temperature of the oceans were to increase, we could say “Aha! That is where deltaQ went” (this is a hypothetical statement. I’m not implying that the temperature of the oceans is not changing). I’m sorry, but all this talk of increased energy without increased temperature seems silly, unless there is some other proposed mechanism for storing the energy. Perhaps it as kinetic energy, or chemical energy or something. Ok. The interesting discussion is one that addresses this unknown energy. This is the temperature rise ‘in the pipeline’. The energy will be converted from wherever form it is currently being stored into some form that will be measured by increased temperature.

My understanding is there are currently some questions about what that ‘other’ form of energy storage is. Correctly identifying it will make this ‘in the pipeline’ stuff go away. There is no pipeline. There is only energy and what affect it is having on our planet.

Heat Flux, the instantaneous (or time derivative if you will) power of energy transfer is measured in watts. The specific heat of liquid water is about 4W · sec/c3 · K. Increase the net Heat Flux by 1W into 1cc of H2O integrated over __4 seconds__ equals ∆1K.

I’m not sure if I got it or not. Is there a particular question you are trying to address with your comment? My question to rhr was how could a change in the time derivative of energy result in no change in energy, unless said change were to change the time derivative of energy to zero. Was that the question you were trying to answer? If so, then no, I don’t get it.

Amanda @35. Problem is that that wasn’t sarcasm. It was a strawman. There was no need for one either. Because R’s statement IS NOT saying that there’s zero heat capacity. This is because R’s statement does not DEMAND zero heat capacity.

The sarcasm would have been better spent on something along the lines “Yeah, when the sun comes up in the morning, the entire day reaches daytime max IMMEDIATELY” which would be

a) sarcastic

b) Obviously silly

c) what R’s comment would actually mean if it were a counter to the comment he was replying to

> If dT/d^2t goes to +0.1 but dT/dt was at that time -3, it would take 30 time units to make the temperatures increase over time.

> For someone claiming engineering and calculus at degree level, it’s worrying that you passed (you did pass didn’t you?) and didn’t understand the second derivative.

I didn’t say increase and neither did the comment that I was referring to. Why are you assuming that increase was the only change in direction that could happen.

if dT/dt is -3 and dT/dt^2 is .1, then for 29 units of time, the energy is decreasing. I consider that a change. My understanding of second derivatives notwithstanding, why don’t you consider that a change? To take your example one step further, during the 30th unit of time, the energy does not change (at that instant, dT/dt is zero). My comment was, if you cause a change in the second derivative, then how could you end up with a net change of zero, unless the change in the second derivative causes the first derivative to be zero? Excuse my thickness, but you still haven’t answered that question.

So, now you no longer need to teach me about the word ‘increase’ or second derivatives, but you just want to make sure I understand the word ‘instantaneous’. Thanks. You are helpful if nothing else. Given that the original comment was quite specific in their reference to “the time derivative of energy” and not the second time derivative of energy, all this talk of second derivatives might have been a distraction, no? And since it was an instantaneous change, there is no time component to the change. That kinda implies that dE/dt^2 is actually zero, doesn’t it (actually, it really would be undefined. Instantaneous change implies a stepwise change. Dividing by zero gives odd results)?

So, I’ll rephrase my original question, since the way I originally phrased it appears to have caused confusion. What point were you trying to make when you stated that an instantaneous change in the time derivative of Energy does not result in a change in Energy? Unless I am wrong, the only way this can occur is if the change to dE/dt causes dE/dt to equal zero.

Your question is specious. The point is that there is zero instantaneous increase in energy. The energy absorbed by an object increases only over some lapse of time. The time a first derivative increase in energy results in an equilibrium increase in temperature (when the rate of energy loss of the object matches the rate of absorption) is dependent on the specific heat of the object absorbing energy. Because the world’s oceans contain a very large volume of water and water has such a high specific heat, and the cumulative power flux differential at the ocean surface is only at present (yet increasing as a second derivative) >1W/m2, thus there is ‘heating in the pipeline’.

Indeed, but that ALSO applies to the thought experiment of “instantaneously adding a bunch more GHG to the atmosphere”. If you instead assume real world conditions – no instantaneous stepwise concentration changes – you take away lots of concerns about undefined derivatives and the like…

> The point is that there is zero instantaneous increase in energy. The energy absorbed by an object increases only over some lapse of time.

ok. I’ll agree with you, but who cares? As soon as a millisecond has passed, the energy absorbed by an object has increased. Practically speaking, your statement only has importance at time t0. Assuming we are talking about some real world process, your point doesn’t seem all that important

> The time a first derivative increase in energy results in an equilibrium increase in temperature (when the rate of energy loss of the object matches the rate of absorption) is dependent on the specific heat of the object absorbing energy.

Actually, I’m not sure I follow this. There are all sorts of things that affect equilibrium of anything. Radiation is proportional to the 4th power of temperature. Conduction and convection and mass transfer are proportional to the first. Mixing affects equilibrium. I’d say that specific heat doesn’t have as much to do with a mass of water absorbing energy reaching some equilibrium as other factors. I’m not sure what a “first derivative increase in energy” means. Energy is energy. The first derivative of energy with respect to time is the rate at which something gains or loses energy. The first derivative of that is the rate at which that rate changes. Could you please just restate that phrase?

> Because the world’s oceans contain a very large volume of water and water has such a high specific heat, and the cumulative power flux differential at the ocean surface is only at present (yet increasing as a second derivative) >1W/m2, thus there is ‘heating in the pipeline’.

Huh? If the flux at the oceans surface is small, that would mean that the amount of energy absorbed is relatively small. Ok, I’m with you there. But are you implying that somehow that ocean water absorbed all those trillions of joules of energy, and the temperature of that water didn’t go up, but that the temperature of the water IS going to rise at some time in the future because of this energy that has been absorbed in the past?

> Do you get it now?

I don’t think so. To be honest, even though you keep addressing me, I don’t think you are talking to me. First, I reply to someone who makes a comment about the first derivative of energy, and you go off on some rant about second derivatives. Then, you make a huge deal about how I say the word ‘change’ and you say I can’t be right because you assume that ‘change’ can only mean ‘increase. Next, you make a statement about how temperature change is dependent on the specific heat of the object absorbing energy, when I am asking a question of someone who states “Heat capacity is a red herring”.

If you really want to try to have an exchange with me, perhaps you could start by just clearly defining what is meant by ‘heating in the pipeline’. And to be honest, stop trying to be such a smart ass. You have proved several times already that you haven’t read what I or the person I asked a question of has said. If you want to talk, go ahead and talk. But stop acting like all you want to do is win an argument regardless of what the argument is.

Lotharsson, you are right. That is why I decided to just ask the commenter what point they were trying to make. I didn’t start this silly discussion about second derivatives. I’d love it if rhr would come back and just explain what point he was trying to make.

“I didn’t say increase and neither did the comment that I was referring to.”

Lets get them reading glasses on, shall we?

“An increment of greenhouse”

Dictionary:

Increment:
1. The process of increasing in number, size, quantity, or extent.
2. Something added or gained: a force swelled by increments from allied armies.
3. A slight, often barely perceptible augmentation.
4. One of a series of regular additions or contributions: accumulating a fund by increments.
5. Mathematics A small positive or negative change in the value of a variable.

If you imagine a constant solar energy flux reaching the earth and that the earth is in equilibrium with that solar flux, then by definition of equilibrium (in this context) the nett energy flux across (say) the outer boundary of the troposphere is zero. In other words there’s a certain rate of solar energy flowing in, and the same rate of radiative energy flowing out.

If you disturb that equilibrium by (say) adding GHGes to the atmosphere) you reduce the rate at which energy leaves the troposphere, **but** the rate at which it *enters* has not changed. Thus, the nett energy flux across the troposphere immediately becomes positive (here defined as a higher rate of energy entering than leaving). Whilst that state of affairs continues the earth must heat up because it is accumulating nett energy.

As it heats, the higher temperatures lead to more higher rates of outgoing radiative energy flow.

In this situation one may say there is “heating in the pipeline” because the heating *must* continue until the earth reaches equilibrium with the solar energy flux once again. In other words, the earth continues get hotter thus increasing the rate of outgoing energy flow, and this process must going until a temperature is reached where once again the rate of energy leaving the troposphere matches the rate of energy entering it. In other words the flux across the troposphere is once again zero.

So a one-off change to atmospheric GHG concentrations can lead to quite a lot of warming in the pipeline, because the earth must accumulate enough energy to get hot enough to balance the slowdown in outgoing radiative energy.

(Of course this leaves out many other real world factors that are changing at the same time, but they don’t change the essential characteristics that lead to the concept of “warming in the pipeline”.)

Unfortunately (as Trenberth lamented to his colleagues), we cannot say so yet. The difference of measured values is 5 or 6 W/m^2 which is unlikely to be real. It is difficult to calibrate absolute levels of radiometers in space, though it seems that the measurements are reliable in terms of temporal variations.

Trenberth adopted a value 0.9 based on balance of evidence: mainly, studies evaluating ocean heat content from synthesis of oceanographic observations, and studies of energy balance in simulations reproducing the climate of the 20th century with coupled ocean-atmosphere climate models. For more information you can find his papers at http://www.cgd.ucar.edu/cas/Trenberth/trenberth-publish.html . The one behind the story of “travesty” is Trenberth 2009 “An imperative for climate change planning: tracking Earth’s global energy”.

> 5 Mathematics A small positive or negative change in the value of a variable.

You do know what ‘negative change’ means, don’t you? Hmmm, I wonder if anyone in this discussion used the word increment in a mathematical context? Go ahead, keep arguing, though. And the smart a** remarks really make you look more clever. Seriously, keep them up.

Is this what you do? You come to websites and try to argue over nits? Because one of the definitions of one of the words in a sentence can be defined as only positive (although thanks to you for providing us a full definition that shows increment can both mean positive or negative changes) you assume it has to be defined that way? It’s obvious you aren’t interested in anything other than the opportunity to make a snarky remark about my reading or math skill, even though you appear determined to show your own inability to read even your own remarks. Who did I piss off to get Luminous and wow commenting back to me without even trying to read anything I or the original commenter said? Is this the definition of ‘troll’?

Geez, I hope I didn’t accidentally spell something wrong, you’ll be telling me to get a refund on my 3rd grade tuition next…

I totally buy your scenario. That seems the only logical definition of ‘heating in the pipeline’ to me. I was just trying to understand what other commenters here meant. For example, your definition has nothing to with specific heat, but others here think that ‘heating in the pipeline’ depends on specific heat. Your definition also makes it sound like ‘heating in the pipeline’ depends on future events. That is, the heating in the pipeline is the energy that will be absorbed in the future, until the temperature of the plant increases so that Qout equals Qin. I was trying to understand what luminous was saying, as it seemed to me that heating in the pipeline referred to energy that had already been absorbed, ie. events in the past.

This actually sounds a lot like what I described in post 41. Did you agree with what I wrote there? After I posted that, I just got a bunch of angry comments talking about second derivatives.

The paper by Ramanathan and Feng, referred to by P. Lewis (August 10, 2010 12:07 PM), uses the term “committed warming” to mean the state where the concentrations of CO2 and other radiatively relevant components are kept constant. It is different from inevitable change, as discussed in RealClimate in March and June (The newer one: http://www.realclimate.org/index.php/archives/2010/06/climate-change-commitment-ii/ ). It is not an easy task for the world to reduce concentration below the present level, of course.

>> “My question to rhr was how could a change in the time derivative of energy result in no change in energy”

> If dT/d^2t goes to +0.1 but dT/dt was at that time -3, it would take 30 time units to make the temperatures increase over time.

You appear to be the first person to make any reference to things increasing or decreasing, and you brought up an example of dT/dt being negative. In that scenario, your scenario, wouldn’t energy be decreasing? Did you just call me a tool for being ambiguous about increases vs. decreases when any reasonable discussion would make it obvious that we were talking about increases? Well, you appear to have started the conversation about decreases, not me. Have you read your own comments?

So, lets review, the original commenter makes a statement about an instantaneous change to the first derivative. This results in a second derivative that is undefined. You ignore that and start talking about positive second derivatives and negative first derivatives. And I need to get a new brain? Please do me a favor and point out which comment I made that referred to any particular direction before you made your very explicit post about decreasing energy!

I agree completely. I had no idea what a second derivative was or how critical it was in this case when it looked like no one was talking about them. You cleared that up. Thanks!

And then this whole ‘increase’ vs. ‘change’ thing. I agree completely. This conversation was nearly incomprehensible until you came in with your positive and negative values of each and your great examples. Here we all were thinking we were talking about one thing, and you cleared it up and showed me that we were all talking about something else. And I appreciate your patient, adult attitude to the whole thing. Out here on the internet, lots of people use their relative anonymity to be total asshats. Not you, you have been great. The picture of restraint and patience. I don’t know how I could have been so confused about what I was talking about. You showed me that second derivatives really were important, worthy of my getting a refund when I had no idea that they had anything to do with the conversation. And then I kept making the mistake of talking about ‘changes’ when you clearly showed that I should have referred to both increases and decreases at random times. And then you were great at pointing out my specific examples when I requested. This whole thing has really put you out and I appreciate you taking the time to set me straight.

I’m not commenting on their definitions, but if I’m not mistaken it’s quite defensible to argue there’s *other* types of heating in the pipeline for several additional reasons. We are primarily talking about temperature very close to the earth’s surface, and the dynamics of the oceans and atmosphere (especially various feedback mechanisms) may act to change that temperature even under scenarios where the nett tropospheric energy flux is zero.